系统故障演化过程的事件故障概率分布熵构建及其性质研究

Construction and properties of event fault probability distribution entropy in system fault evolution process

为研究系统故障演化过程带来的系统功能状态的不确定性,提出事件故障概率分布熵的概念和计算方法。系统故障演化过程的不确定性来源于事件故障概率分布和演化过程本身的不确定性,可等效为概率分布和演化的混乱性。基于上述考虑,借助信息熵的思想建立事件故障概率分布熵,对演化过程中事件故障概率分布的变化混乱程度进行度量。考虑事件故障概率分布特征,确定了分布熵模型的各参数,给出了模型推导过程,建立了分布熵表达式。研究表明:分布熵具有对称性、确定性、非负性、扩展性、可加性和极值性,符合信息熵规则;分布熵与因素数量、因素值域的等距划分点数量、故障概率变化程度均存在正相关性。通过实例演示了事件故障概率分布熵的计算过程,得到了不同事件分布熵的大小关系,表明了不同事件对系统功能状态不确定性的影响。为下一步建立系统故障演化过程的熵理论提供基础。

To study the uncertainty of the system function state caused by the system fault evolution process,the concept and calculation method of event fault probability distribution entropy are proposed.The uncertainty of the system fault evolution process comes from the uncertainty of event fault probability distribution and the evolution process itself,which can be equivalent to the chaos of probability distribution and evolution.It is necessary to study the uncertainty of evolution results by determining these chaoses.Based on the above considerations,the event fault probability distribution entropy is established with the help of the idea of information entropy to measure the change and chaos of the event fault probability distribution in the evolution process.Considering the characteristics of event fault probability distribution,the parameters of the distribution entropy model are determined,the derivation process of the model is given,and the expression of distribution entropy is established.The boundedness of distribution entropy is discussed and the maximum and minimum values of distribution entropy are determined.The research shows that the distribution entropy has symmetry,certainty,nonnegativity,expansibility,additivity,and extremum,which conforms to the rule of information entropy;the distribution entropy is positively correlated with the number of factors,the number of equidistant dividing points of factor value range and the change degree of fault probability.It is very beneficial to establish the related methods of distribution entropy based on the existing concepts,definitions,and methods of information entropy.The calculation process of event fault probability distribution entropy is demonstrated by an example,the relationship between the distribution entropy of different components is obtained,and the influence of different components on the uncertainty of the system function state is shown to obtain the quantitative description of the uncertainty and chaos of the event fault probability distribution.It provides a basis for establishing the entropy theory of the system fault evolution process in the next step.